Acyclic database schemes are schemes that contain a single acyclic join dependency ( a join dependency is a relationship governing the joining of tables of the database ) and a collection of functional dependencies; a number of researchers, including Yannakakis, pointed out the usefulness of these schemes by demonstrating the many useful properties they had : for example, the ability to solve many acyclic-scheme based problems in polynomial time, whereas the problem could easily have been NP-complete for other schemes.
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A simple application of functional dependencies is "'Heath s theorem "'; it says that a relation " R " over an attribute set " U " and satisfying a functional dependency " X " ?! " Y " can be safely split in two relations having the Unions of attribute sets are customarily denoted by mere juxtapositions in database theory . ) An important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation.
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A simple application of functional dependencies is "'Heath s theorem "'; it says that a relation " R " over an attribute set " U " and satisfying a functional dependency " X " ?! " Y " can be safely split in two relations having the Unions of attribute sets are customarily denoted by mere juxtapositions in database theory . ) An important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation.
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R is a relation and A, B, C be subsets of attributes, of R . A be a candidate key of R . There's a transitive functional dependency ( TFD ) on R if the FDs : A-> B, B-> C, and A-> C all hold on R . Each FD in the TFD can be either trivial or non-trivial FD . ( Just for completeness : the FD A-> B is trivial if B is a subset of A, otherwise it's non-trivial .)
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